"The families have asked for privacy. Our thoughts are with them at this difficult time.

"Foreign Office staff remain in close contact with all the families.

"We continue to do everything we can for the release of the other hostages."

The Oxfordshire Coroner has been informed and will open and adjourn inquests into the deaths before releasing the men's bodies to their families so their funerals can be held, the spokesman added.

Mr Creswell, originally from Glasgow, and Mr Swindlehurst, from Skelmersdale, Lancashire, were among a group of five Britons kidnapped in Baghdad on May 29, 2007.

A group of 40 armed men wearing police uniforms seized the hostages, including IT consultant Peter Moore, from Lincoln, and two guards identified only as Alan from Scotland and Alec from South Wales, at the Iraqi Finance Ministry in the capital.

In recent weeks, hopes had risen that the men could soon be freed after the release of a senior Iraqi insurgent at the beginning of the month.

But that hope was dashed when the bodies of Mr Creswell and Mr Swindlehurst were handed over to authorities late last Friday.

Jan Beattie, a friend of Mr Creswell, made a statement on behalf of all five families at the time, speaking of their "profound grief".

She said: "We are deeply stunned and saddened by the tragic and upsetting news of the deaths of Jason Creswell and Jason Swindlehurst.

"We ask those still holding Alec, Alan and Peter to release them and allow them to return home to their families as soon as possible."

In February last year, a video broadcast by Dubai-based TV station Al-Arabiya showed a bearded and tired-looking Mr Moore asking Prime Minister Gordon Brown to free nine Iraqis in exchange for the British hostages.

He said: "All I want is to leave this place. I tell Gordon Brown the matter is simple: release their prisoners so we can go."

Five months later, the hostage-takers claimed that one of the two Jasons had committed suicide.

Mr Moore's father Graeme, 59, has angrily condemned the Government's handling of the case, describing Foreign Secretary David Miliband as a "total waste of space".

The delivery driver from Leicestershire said he continued to hope his son was alive, but described the wait for any news as "torture".

Mr Brown said he has told the Iraqi Prime Minister the Government is determined to secure the release of the remaining captives.

Responsibility for the kidnapping was at first pinned on Muqtada al-Sadr's Mahdi Army.

It was thought to be a retaliatory attack for the killing by British forces of the militia's commander in Basra, southern Iraq, a week earlier.

But al-Sadr's followers denied responsibility and suspicion fell on splinter groups which the US believes are controlled by Iran.

The release of leading Shiite insurgent Laith al-Khazali by US forces on June 6 had sparked fresh hopes the Britons could be freed.

Al-Khazali is a senior member of Asaib Ahl al-Haq, or the League of the Righteous, which has been linked to the kidnapping.